Question 177462
Your equation is in the form {{{ax^2 + bx + c = 0}}}, where {{{a = 6}}}, {{{b = 4}}}, and {{{c = -3}}}.  The discriminant is the part of the quadratic formula <large>(</large> {{{x = (-b +- sqrt( b^2-4ac ))/(2a) }}}<large>)</large> that is under the radical, namely {{{DELTA = b^2-4ac}}}.  Just plug in the values and do the arithmetic.


{{{DELTA > 0}}} means that you have two distinct real number roots.  (Your answer C)


{{{DELTA = 0}}} means that you have two identical real number roots.  Alternatively, it can be said that you have one real number root with a multiplicity of 2.  (Your answer A)


{{{DELTA < 0}}} means that you have a conjugate pair of complex roots of the form {{{a+-bi}}} where {{{i}}} is the imaginary number defined by {{{i^2=-1}}} (Your answer B)